Thick slime at egg laying?! Should I be alarmed

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My duck Olive is new to this whole egg laying thing, she's been at it about 2 weeks now and since she's a Runner that hasn't amounted to much. I know that beginning layers have lots of hiccups but she is laying oddballs more often than not! She squeezed out an immense double yolker (bigger than her head, which hurt her vent but she's fixed up now) and has done a fart egg smaller than what my seramas usually lay. No two eggs are the same size or shade of off-white. Do ducks just have an extra dramatic start-up??

On to the more urgent question: today she came flopping uncomfortably in to my room and SHOT an egg out of her bum like a projectile. With this firing came a thick string of snot-like slime! It seemed very albumen-like but she was on a pile of clothes (I really need a hamper, sigh) so I didn't get a good look. It was soaked up while I was busy checking her vent to make sure she was ok. Nothing like a bloom, there had to be at least a tablespoon of the stuff. The egg itself is leathery and has no yolk. It also does not have any perforations, so despite the softness I do not think it is the source. She usually lays in the morning, and I in fact already gathered an egg from her nest today! This is the second time it has seemed like she laid twice in a day, though we have not had definite proof, the theory being she might just be uncovering an egg she laid and buried.

Should I be worried about that slime, or do ducks just have very slimy laying? I know reproductive problems require urgent care but I -just this week- spent $350 at the vet treating a chicken with an eye tumor, and she is not even done. I don't want to rush off to spend more money I hardly have just to be told "oh yeah, ducks snotting from their butts is totally normal."

 

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I put her in to the bath because she was seeming entirely too quiet (she is usually a constant stream of noise) and seemed tense. She popped out ANOTHER leathery egg. I think it was albumen from this egg that shot out with the first one an hour prior. We're taking her to the vet first thing in the morning since they are now closed.

 

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Had x-rays at the vet to see if there was internal laying going on, and there did not appear to be! Her egg waiting to be laid today will also be soft, though. Olive also did not feel very well at all last night, and while she seems improved today she is still a bit off. Since we know at least one egg was broken inside her and this one has a breaking risk as well we are putting her on aggressive antibiotics to stave off peritonitis, as well as an anti-fungal against thrush since she is so young.

Laying soft eggs is common for new layers but having so many isn't normal, that is calcium deficiency. She doesn't seem to be enjoying her oyster shell so she was prescribed a set of liquid calcium to help her in an immediate and we are switching her to a duck specific layer feed. We can't give her liquid calcium forever, so I need to find a way to make calcium she regulates the intake of more appealing to her.